The Feel Good Song Formula

Update 22/9/2016

I see the Feel Good Formula has been getting some attention again! Since last year, we have repeated this study in a Dutch sample, but now with a continuous rating (i.e. “How ‘feel good’ is this song on a scale from 1-100?”) That allows for a far better statistical model. Fortunately, the results do confirm the earlier work (i.e. Don’t Stop Me Now is still firmly in the Top 3). The full Dutch list can be found here (of course, it is edited for radio-friendliness). For those of you interested, based on the Dutch data, the full regression formula is:

Rating = 60 + (0.00165 * BPM – 120)^2 + (4.376 * Major) + 0.78 * nChords – (Major * nChords)

Where BPM is beats per minute (tempo), Major is 1 if the song is in a major key and 0 is the song is in a minor key, and nChords is the number of chords in the song (including modulations etc.) The formula basically says we generally like songs with a tempo that deviates from the average pop song tempo, that are in a major key, and are a bit more complex than 3 chord songs, UNLESS the song is in a major key.

If you’re in the UK, maybe you have seen or heard something about the ultimate feel good song formula uncovered by a real scientist with a somewhat unpronouncable name from a university with an equally unproncouncable name. Well, that scientist was yours truly! I got quite some questions about this feel good formula and how I ‘uncovered’ it, so here’s a short blog post on it!

The research was commissioned by a British electronics brand called Alba, who did a large customer survey in the UK and the Republic of Ireland, asking respondents for their musical preference, where they got their musical taste from, and, most importantly, their favourite songs to improve their moods. Probably given my background is using music as a mood manipulation (a.o. in Jolij & Meurs, 2011) my name popped up when they were looking for an academic to help them analyze this enormous dataset. Basically, they asked me whether I could find a general pattern in the songs that respondents reported as ‘feel good songs’, and whether they could use this pattern to come up with a ‘formula’. I found this an interesting challenge, so I said yes. One week later I received the data, and I could get to work.

A ‘feel good song’ is rather tricky to define. Music appreciation is highly personal and strongly depends on social context, and personal associations. In that respect, the idea of a ‘feel good formula’ is a bit odd – factoring in all these personal aspects is next to impossible, in particular if you want to come up with a quantitave feel good formula. Basically, what you need are song features that you can express in numbers.

Fortunately, music does have specific features that are known to play an important role in emotional reception of songs. In particular these are mode (major or minor) and tempo. So, the first thing I did was to identify all unique songs that respondents listed as ‘feel good’, and find the scores of these songs to determine key and tempo. Next, I looked at some additional variables, such as season in which the song was released, genre, lyrical theme, and overall emotionality of the lyrics.

So, now I’d got myself a big matrix with numbers. Now what? Originally, I planned to fit a linear mixed model to predict whether a song is a feel good song or not. A mixed model would be ideal – it would allow me to include a random factor for song, or even for respondent, and thus correct (somewhat) for individual differences such as social context, associations, and what more. Unfortunately, the list I got only listed feel-good songs. That’s a problem for an LMM, because you cannot fit a model if your outcome variable (feel good-song or not a feel good-song) has zero variability. Same thing for a machine learning algorithm – you need exemplars of both categories you want to classify. And I had just one…

The perfect solution is of course to come up with a baseline of songs that were not classified as ‘feel good songs’. Given I had only a very limited amount of time for this analysis, that was not feasible. I therefore decided to have a look at the means and in particular distributions of the key variables tempo and key to see if they would differ from the average pop song. The pattern was very clear – the average tempo of a ‘feel good’-song was substantially higher than the average pop song. Where the average tempo of pop songs is around 118 BPM, the list of feel good songs had an average tempo of around 140 to 150 BPM. Next I had a look at key (major or minor). Again a very clear pattern: only two or three songs were in a minor key, the rest was all in a major key. Of course, the proof of the pudding is in eating. I’ve created four short clips, two in a major key (C G Am F, the famous I-V-vi-IV progression), and two in a minor key (Am Am Em Bm), each at 118 BPM and 148 BPM, with a 4-to-the-floor beat under them. Listen to the differences, and decide which one would make the best feel good song.

Of course, a song is more than its score. I have also looked at lyrical themes. Predominantly, the feel good songs were about positive events (going to a beach, going to a party, doing something with your love, etc.) or did not make sense at all.

At the end of the story, I had to cook up a formula. My client had asked me to come up with a formula for PR-purposes: a formula can nicely explain the ‘main’ ingredients of a feel good song at a glance. The formula I came up with takes the number of positive lyrical elements in a song, and divides that by how much a song deviates from 150 BPM and from the major key. It’s not perfect at all – it’s mostly an illustration (all four clips I posted here would score 0 on my formula, simply because they have no lyrics, for example).

So, how to get from the ‘formula’ to the list of ultimate feel good songs? I had little to with that actually – we simply took the most often mentioned song per decade. Given that these modal feel good songs contribute to the averages, of course they fit the ‘formula’ reasonably well.

All in all, this was a fun assignment to do. Of course the main purpose for Alba was marketing, but that’s ok. They are to commended for doing this in such a data-driven fashion, in stead of making something up. Is this hardcore science? No, it’s data crunching – for me as a scientist, it’s useful because I now have a list of songs I can use for mood manipulations. However, the truly interesting questions are still open. Is this model predictive, that is, can it be used by composers to write specific feel good songs? What is so special about the major key that it makes us feel good? Why do fast songs work so well? Stuff to work on in the future – and maybe the most exciting thing about this commission is the sheer amount of responses I got from people interested in this work, and interested in finding an answer to the questions I mentioned earlier. I’m sure you’ll be hearing more about this topic from us in the near future!

PS: as this research was a private commission, I am afraid there is not going to be a peer-reviewed publication in the short term, nor am I at liberty to release the data. However, the reception of this work has inspired me to put my music-related work on top of my to-do list. Watch this space for more music research soon!